Abstract:
The use of a replicated Latin square design for reference material homogeneity assessment is illustrated by application to a homogeneity study of eight high-purity organic materials certified for melting point. The design controlled for both a three-level location effect and a run effect. Variance components were extracted using mixed effects modelling using a restricted maximum likelihood method. An alternative classical ANOVA calculation is also given. Once a need for blocking and randomisation is admitted, the use of the replicated Latin square design adds little in
terms of operating complexity, and with current software, the analysis of the resulting data is straightforward. The effect of appreciable numerical rounding by the instrument software was investigated and shown to be acceptable for the particular example. Estimation of the scale of location and run effects showed that in this example the location effect was both statistically and practically significant, while the run effect was not statistically significant at the 95% level of confidence. The design allowed unbiased estimates of between-unit variances in the presence of both interfering effects.
Highlights:
- This approach for assessment of homogeneity was chosen, because the measurement facility used for certification was not appropriate. Firstly, the run time for individual observations would be too long and secondly, the required mass for an aliquot was in the order of 2 g, which was too large for a useful homogeneity study. End users of melting point CRMs typically use the materials to check capillary equipment that uses samples sizes in the 2 to 10 mg range.
- The bench top instrument used could accept up to three samples per temperature run in three distinct locations, which added both a possible run effect and a location effect as nuisance effects to the study.
- The paper demonstrates the use of replicated 3 X 3 Latin square design for the elimination of two nuisance effects during a homogeneity study.
- Increasing the number of units of material to 12 and replicating the design four times gives effective degrees of freedom comparable to the recommendation of ISO Guide 35.
- Three ways for the extraction of the main effects and relevant variance components from the replicated Latin square design are presented, i.e. using software to apply a classical ANOVA, the manual construction of an ANOVA table and using mixed effects modelling software.
- The effect of the rounding of the instrument used on the calculated variances is also evaluated.
- A very useful appendix is provided for the manual calculation for a replicated Latin square design with one fixed effect.
Citation:
Ellison, S.L.R., Grimes, N., Fardus, F. et al., “Use of a replicated Latin square design in a homogeneity test for high purity organic melting point standards”, Accred Qual Assur (2012) 17: 283.